A slot line waveguide that consists of two equal-width lines induces local magnetization dynamics around each line. Spin waves emitted from the local magnetization dynamics propagate and interact with the other side of the local magnetization dynamics. We have studied the high frequency waveguide’s size dependence of magnetization dynamics to understand the interaction. In our previous study, we reported the interaction for the case of which the magnetic field applied to the film plane [1,2]. We have revealed that the interaction induces the resonantly excited magnetization dynamics, and the excitation condition is determined by the design of lines. In this paper, we study the magnetization dynamics induced by a slot line waveguide with the applied magnetic field perpendicular to the plane. The spin wave mode for our previous study was magnetostatic surface spin waves (MSSW) [3]. When the magnetic field is applied normally to the film plane, forward volume magnetostatic spin waves (FVMSWs) are induced [3]. YIG (111) single crystal thin films with the thickness of 10 µm were epitaxially grown on gadolinium gallium garnet (GGG) (111) single crystal substrates. All the slot line waveguides were fabricated directly on the YIG (111) single crystal thin film using a combination of photolithography, Ar ion milling and sputtering techniques (as) shown in Fig. 1 (a). The line width and the gap between the lines in the waveguides were systematically varied. The high frequency power response was evaluated with a vector network analyzer. The input signal strength was fixed at 0 dBm for all the measurements and the frequency was set at a frequency between 3.0 and 13.0 GHz for each measurement. Figs 2 (a) and (b) show the maginetization dynamics at 7.0 GHz dependent on the line width and the gap, respectively. Multiple peaks were observed for all the measurement conditions. The magnetic field at the peak of magnetization lowered with the increase of the line width. The number of peaks also increased with the line width as well as the distance between lines. It should be noted that the number of peaks is much larger compared to the measurement for in plane [2]. We assume this is caused by the shorter wavelength of spin waves for FVMSW compared to MSSW, which enhances the periodicity of the condition for the same phase between local magnetization dynamics and spin waves. Those experimental results indicate that artificially controlled magnetization dynamics can be effectively induced with the use of FVMSW. We thank GRANOPT Co,Ltd. for their support of YIG single crystal thin films. This work was supported in part by JSPS KAKENHI Grant Number JP18K14114. This work was supported in part by CSRN, Tohoku University. A part of this work was carried out at Nano-Fabrication Support Laboratory, Yamaguchi University supported by "Nanotechnology Platform Project" of the Ministry of Education，Culture，Sports，Science and Technology (MEXT)，Japan. A part of this work was carried out at Nano-Fabrication Support Laboratory, Yamaguchi University supported by "Nanotechnology Platform Project" of the Ministry of Education，Culture，Sports，Science and Technology (MEXT)，Japan.

**References:**

[1] Tetsunori Koda, Sho Muroga, and Yasushi Endo. “Artificial control of magnetization dynamics via spin waves by slot line waveguide.” in Digests of Intermag 2020, session GE-5, Montreal, Canada, 4-8 May, 2020. [2] Tetsunori Koda, Sho Muroga, and Yasushi Endo, “Synchronized excitation of magnetization dynamics via spin waves in Bi-YIG thin film by slot line waveguide” Appl. Phys. Lett. 116, 102403 (2020). [3] A A Serga, A V Chumak, and B Hillebrands. “YIG magnonics” J. Phys. D: Appl. Phys. 43 264002 (2010).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/110cf3dc099d22f66347a0a16090ef60.jpg)
Schematic View of measurement set up for magnetization dynamics using a slot line waveguide. Magnetic field is applied to perpendicular to the plane.

![](https://assets.underline.io/uploads/markdown_image/1/image/5f11489dab4811544ec888fa8595d88e.jpg)
Magnetization dynamics measured at 7.0GHz for (a) Line’s width dependence and (b) Line’s gap dependence.

 Enhancement of magnetization dynamics via spin waves by slot line waveguide for perpendicularly magnetized yttrium iron garnet

The control of magnetization dynamics is an important issue for the development of high-frequency devices based on spintronics. There are several ways to excite magnetization dynamics. In our previous study, we reported the amplification of magnetization dynamics derived from the interaction between local magnetization dynamics and spin waves by using a slot line waveguide [1]. In this paper, we report the study on the evaluation of the interaction by measuring ST-FMR. The spin orbit torque is caused by the spin current induced by the spin hall effect in ferromagnetic and non-ferromagnetic bilayer system. The ST-FMR is originally used for the estimation of the spin orbit torque via the measurement of the spin hall magneto resistance. We found that the ST-FMR signals for the samples described below delivered information on the interaction between local magnetization dynamics and spin waves. Fig.1 shows the sample structure and measurement set up for the ST-FMR. We used yttrium iron garnet (YIG) as a ferromagnetic layer. Coplanar waveguides were prepared on the YIG film. The signal line consisted of Cu layer (200 nm) , and was partially replaced by 10nm thick Pt layer. In the separated Pt areas, additional local magnetization dynamics was excited by the spin orbit torque, emitting spin waves. The distance between Pt areas was systematically varied, leading the change of the strength of the interaction between the local magnetization dynamics and spin waves at the Pt areas. Fig.2 shows the distance between Pt areas dependence of ST-FMR signal measured at 7.0 GHz. The sample with one Pt shows symmetrical peaks. On the other hand, the samples with two Pt areas indicate that the asymmetry of the peaks changes with the distance of Pt areas. The symmetry and asymmetry of the peaks reflect the contribution of torques to the magnetization dynamics from the spin orbit torque and RF magnetic field respectively at Pt areas [2]. It should be noted that the strength of RF magnetic field was fixed for all the samples, meaning that the increase in the asymmetry was caused by an additional torque to the magnetization. Another factor is speculated from the interaction between local magnetization dynamics and spin waves because the direction of the torque for the interaction is considered the same as the direction for the RF Oersted field, leading the asymmetry of the peak for the ST-FMR measurement. The asymmetry of the curve showed strong dependence on the distance between Pt areas, reflecting the strength of the interaction. Those experimental results give a way to design the artificially controlled magnetization dynamics effectively. We thank GRANOPT Co,Ltd. for their support of YIG single crystal thin films. This work was supported in part by JSPS KAKENHI Grant Number JP18K14114. This work was supported in part by CSRN, Tohoku University. Part of this work was carried out under the Cooperative Research Project Program of the Research Institute of Electrical Communication, Tohoku University. A part of this work was carried out at Nano-Fabrication Support Laboratory, Yamaguchi University supported by "Nanotechnology Platform Project" of the Ministry of Education，Culture，Sports，Science and Technology (MEXT)，Japan.

**References:**

[1] Tetsunori Koda, Sho Muroga, and Yasushi Endo, “Synchronized excitation of magnetization dynamics via spin waves in Bi-YIG thin film by slot line waveguide” Appl. Phys. Lett. 116, 102403 (2020). [2] Luqiao Liu, Takahiro Moriyama, D. C. Ralph, and R. A. Buhrman, “Spin-Torque Ferromagnetic Resonance Induced by the Spin Hall Effect” Phys. Rev. Lett., 106, 036601 (2011).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/163119439d61e9013a174ed3d596d259.jpg)
Schematic view of measurement set up for ST-FMR measurement. A part of the signal line consists of Pt layer for inducing the spin orbit torque.

![](https://assets.underline.io/uploads/markdown_image/1/image/72e2a7835f5ae71297581d9613fbf769.jpg)
Gap of Pt areas dependence of ST-FMR signal measured at 7.0 GHz.

 Evaluation of interaction between local magnetization dynamics and spin waves measured by ST-FMR

I. INTRODUCTION Ferromagnetic resonance (FMR) measurement technique is well known to be one of the important methods to evaluate the dynamic magnetic properties such as the effective saturation magnetization, damping constant, and so on, of magnetic thin film materials [1]. Recently, a broadband FMR (B-FMR) measurement technique with a coplanar waveguide (CPW) and a vector network analyzer (VNA) has been widely used to investigate them [2]-[4]. The reason for this is that the films are excited in a very wide range of RF frequency changing external magnetic field intensity and its high sensitivity allows for downsizing of the samples to the micro-scale, which provide detailed information on very thin films subjected to practical use under a variety of circumstances. In general, for FMR measurement technique, it is pointed out that the non-uniform magnetization precession mode occurs by the applied direction of external magnetic field. However, for the B-FMR measurement technique, this problem still remains an open question. Herein, we chose Fe-M binary alloys as magnetic thin film materials, investigated the in-plane and out-of-plane dynamic magnetic properties of Fe-M binary alloy thin films using the B-FMR measurement technique, and further discussed the difference between these properties in their films by the applied direction of external magnetic field in detail. II. EXPERIMENTAL PROCEDURES 10-nm thick Fe-M (M=Ni, Si, Co, and Ga) binary alloy thin films were fabricated by DC magnetron sputtering onto glass substrates. These film compositions were determined by energy dispersive x-ray spectroscopy (EDX), while the crystallographic structure of these films was performed using the high-angle XRD analysis and TEM observation, indicating that all film structures are polycrystalline and bcc phase. As for the dynamic magnetic properties of these films, the in-plane and out-of-plane effective saturation magnetization (4πMs,eff, //, 4πMs,eff,⊥) and the in-plane and out-of-plane effective damping constants (α//, α⊥) were evaluated by the B-FMR measurement technique. The external magnetic field was applied parallel to the CPW plane and swept between -0.01–0.3 T at various resonance frequencies. On the other hand, 4πMs,eff,⊥ and α⊥ of the films were determined in an external magnetic field applied perpendicular to the CPW plane swept between 1.4–3.3 T at various resonance frequencies. These measurements were performed at room temperature. The other magnetic properties of these films were already described in [4], [5] in detail. III. RESULTS AND DISCUSSION 4πMs,eff, //, 4πMs,eff,⊥, α//, and α⊥ of 10-nm thick Fe-M (M=Ni, Si, Co, and Ga) thin films are summarized in Table 1 and 2. As be noticed in Table 1, 4πMs,eff, // values of these films became higher or lower than those of saturation magnetization (4pMs) evaluated by VSM, which might be attributed to the appearance of negative or positive surface anisotropy. On the other hand, 4pMs,eff,⊥ of these films almost agreed with those of 4πMs evaluated by VSM, meaning that the easy magnetization direction of every film is in the film plane. As for the effective damping constant (Table 2), in case of M=Ni, α// value was almost equal to that of α⊥, indicating that the intrinsic damping can be obtained regardless of the external magnetic field direction. On the other hand, in case of M=Si, Co, and Ga, these damping depend on the external field direction, and these α// values were higher than those of α⊥. The reason for these differences might be that the non-uniform magnetization precession mode appears by magnetic inhomogeneities such as the two-magnon scattering, the anisotropy dispersion, and so on when the external magnetic field is applied in the film plane. On the basis of these results, it is suggested that the external magnetic field direction must be seriously selected by the kind of magnetic materials as their effective damping constants are evaluated by the B-FMR measurement technique. ACKNOWLEDGEMENT The authors thank Prof. Satoshi Okamoto, and Associate Prof. Nobuaki Kikuchi at Tohoku University for performing the photo lithography and measuring XRD diffraction patterns. This work was supported in part by KAKENHI (JP17H03226) from MEXT, Japan. This work was supported in part by CSIS, CSRN, and CIES, Tohoku University. This work was also supported in part by the ASRC in Japan.

**References:**

[1] J. H. E. Griffiths, Nature 148, 670 (1946)., [2] G. Counil et al., J. Appl. Phys. 95, 5646 (2004). [3] M. Toda et al., J. Magn. Soc. Jpn. 31, 435 (2007). [4] Y. Endo et al., J. Appl. Phys. 109, 07D336 (2011). [5] Y. Kawabe et al., Trans. Magn. Soc. Jpn. 3, 34 (2019).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/4fc57e3b82465a0fe4857ce200b27537.jpg)
Table 1. Comparison between the in-plane and out-of-plane effective saturation magnetization (4πMs,eff, //, 4πMs,eff,⊥) for Fe-M binary alloy thin films.

![](https://assets.underline.io/uploads/markdown_image/1/image/b17d7443a35e49fed8dce0227d6c370d.jpg)
Table 2. Comparison between the in-plane and out-of-plane effective damping constants (α// and α⊥) for Fe-M binary alloy thin films.

 Study on comparison between in-plane and out-of-plane dynamic magnetic properties for Fe-M binary alloy thin films

I. INTRODUCTION With the rapid development of new, ultra-low power spin-based devices such as magnetic random access memory (MRAM), spin logic, and so on, the magnetization dynamics in amorphous Co-Fe-B thin films has been studied intensively both from the fundamental and application points of view. In particular, a Gilbert damping constant (α), which describes the strength of damping torque, is one of the most important parameters to understand the dynamics. Until now, other groups reported α of amorphous Co-Fe-B thin films with various thicknesses and B compositions [1],[2], while details about the effect of Co compositions on α of these films have not been understood fully. In addition, the correlation between α and other magnetic parameters such as magnetic anisotropy, magnetostriction and so on still remains unclear. Herein, we evaluate the soft and high-frequency magnetic properties of Co–Fe–B thin films with various Co compositions, and discuss in detail the effect of Co composition on these magnetic properties of these films. III. EXPERIMENTAL PROCEDURES 10-nm thick CoxFe80-xB20 (Co–Fe–B) thin films (0 ≤ x ≤ 80) were fabricated by RF sputtering onto glass substrates. Co composition (x) was determined by energy dispersive x-ray spectroscopy (EDX) and the saturation magnetization estimated from VSM. The identification of the crystallographic structure of Co–Fe–B films was performed using the high-angle XRD analysis and TEM observation. These analyses indicated that every film structure is amorphous regardless of Co composition. The soft magnetic properties of Co–Fe–B films and the in-plane M–H curves were measured by VSM. The measurement of magnetostriction was performed using a thin-film magnetostriction measurement system (Toei Scientific Industrial Co., Ltd), which used an optical-cantilever method to detect sample deflection caused by magnetostrictive effect. The saturation magnetostriction (λs) of these films was evaluated using this system in an external magnetic field of 0.0 - +13.5 kA/m, which was sufficiently strong to magnetically saturate the films. The high-frequency magnetic properties were evaluated using a broadband ferromagnetic resonance (B-FMR) measurement technique with a coplanar waveguide (CPW) and a vector network analyzer (VNA). These measurements were performed at room temperature. III. RESULTS AND DISCUSSION Figure 1(a) shows the dependence of saturation magnetostriction (λs) on Co composition (x) for Co–Fe–B thin films. λs increased when Co composition increased up to 15 at.%, kept constant when Co composition was 15–40 at.%, and further decreased markedly when Co composition was above 40 at.%. This feature was almost similar to that of the Co-Fe–B bulk alloy, while their values were higher than those of these alloys [3]. The reason for this may be attributed to the compressive stress induced in the film plane during the film deposition. To understand the high-frequency magnetic properties of Co–Fe–B thin films, the parameters related to these properties [e.g., effective in-plane damping constant (α//) and magnetic inhomogeneous broadening at zero frequency (ΔH(0))] were estimated and are summarized in Fig. 1(b) as a function of Co composition (x). α// decreased to a minimum at the Co composition of 15 at.%, increased to approximately 0.0096 when Co composition was increased up to 30 at.%, again decreased to approximately 0.0062 for the Co composition between 40–50 at.%, and further markedly increased to a maximum at 80 at.%. The α// values for the Co composition of 30 and 80 at.% were twice or three times as high as those for other Co compositions, respectively. On the other hand, for ΔH(0), the trend was almost similar to that of α//. The values for the Co compositions of 30 and 80 at.% were much higher than those for other Co compositions. Therefore, these results suggest that the magnetic inhohmogeneities such as the anisotropic dispersion, two-magnon scattering, and so on mainly influences on the high-frequency magnetic properties of Co–Fe–B thin films. ACKNOWLEDGEMENT The authors thank Prof. Satoshi Okamoto, and Associate Prof. Nobuaki Kikuchi at Tohoku University for performing the photo lithography and measuring XRD diffraction patterns, and Mr. Osamu Mori, Mr. Takashi Oizumi, Mr. Shigeyuki Sato, and Mr. Ryoichi Utsumi of Toei Scientific Industrial Corporation for measuring magnetostriction. This work was supported in part by KAKENHI (JP17H03226) from MEXT, Japan. This work was supported in part by CSIS, CSRN, and CIES, Tohoku University. This work was also supported in part by the ASRC in Japan.

**References:**

[1] M. Oogane et al., Jpn. J. Appl. Phys. 45, 3889 (2006). [2] X. Liu et al., J. Appl. Phys. 110, 033910 (2011). [3] R.C. O’Handley, Solid State Comm. 21, 1119 (1977).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/61c7e0f4781eb9c38d8e77db3d1af2e9.jpg)
Fig. 1. (a) Dependence of saturation magnetostriction (λs) on Co composition (x) for Co–Fe–B thin films. The dotted line shows λs of the Co-Fe–B bulk alloy reported in Ref.[3]. (b) Change in the effective in-plane damping constant (α//) and magnetic inhomogeneous broadening at zero frequency (ΔH(0)) of Co–Fe–B thin films with Co composition (x).

 Study on the soft and high-frequency magnetic properties of amorphous Co-Fe-B thin films with various Co compositions

With the rapid improvement of electromagnetic (EM) equipment, the high-frequency (HF) soft magnetic films have been studied intensively as HF components such as a film type inductor, an electromagnetic noise suppressor sheet, and so on.[1, 2] In particular, the nano-granular films are well-known as one of the best choices as HF components, which can prevent the ensuing plunge in electrical resistivity as ferromagnetic resonance frequency (fFMR) increases. Herein, we select Co-Sr-F nano-granular films as the material of HF components and investigate their structure and magnetic properties in detail. The structure is nanocomposite, that is, Co nano-granules are evenly dispersed in a ceramic matrix. TEM observations indicate Co nano-granules change from a spherical to a columnar shape as the Co content increases. The electrical resistivity decreases from 109 to 104 μΩ*cm with a steep around 50~55 at.% of Co content as the Co content increases because of the change in the morphology of the film. In the range of Co content above 50 at.%, their coercivities are obtained and their saturation magnetizations (Ms) increase linearly(Fig.1). These results indicate that the films are ferromagnetic in the range of Co content above 50 at.%. To clarify fFMR of these films, the change in permeability of these films with frequency is measured, and the observed fFMR is summarized in Fig. 2 as a function of Co content. For Co content between 51~55 at.% (stage I), fFMR remains constant around 4.8 GHz, while, for Co content above 55 at.% (stage II), fFMR increases to 12 GHz monotonically. These behaviors can be explained by the change in the morphology of Co nano-granules. Namely, in stage I, as Co nano-granules are spherical, Kittel formula[3] is expressed as fFMR=γHz (γ is the gyromagnetic ratio). In stage II, as Co nano-granules are columnar, Kittel formula is described as fFMR=γ(Hz+1/2MS) and fFMR increases linearly with the increase of Ms. Therefore, these results demonstrate fFMR and film morphology correlates each other apparently, and suggest that Co-Sr-F nano-granular films are one of the candidates for HF components.

![](https://assets.underline.io/uploads/markdown_image/1/image/95284d1c80b5b322b200c42bcb5efff8.jpg)

Fig. 1 Magnetization curves of Co-Sr-F nano-granular thin film.


![](https://assets.underline.io/uploads/markdown_image/1/image/bfe412a99934f4776922a184262e4281.jpg)

Fig. 2 The dependence of fFMR on Co content.

Relationship between morphology and soft-magnetic properties of Co-Sr-F nano-granular films

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Presentations

Enhancement of magnetization dynamics via spin waves by slot line waveguide for perpendicularly magnetized yttrium iron garnet

Evaluation of interaction between local magnetization dynamics and spin waves measured by ST-FMR

Study on comparison between in-plane and out-of-plane dynamic magnetic properties for Fe-M binary alloy thin films

Study on the soft and high-frequency magnetic properties of amorphous Co-Fe-B thin films with various Co compositions

Relationship between morphology and soft-magnetic properties of Co-Sr-F nano-granular films